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Cambridge Prelim MX1 Textbook Marathon/Q&A (2 Viewers)

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

for integral -e to -2 of 1 -3x^2 / x - x^3 dx

I get using the result integral f'x / fx dx = log(fx)

the answer

log ( 6 / e^3 - e )

but in the answer it says log 6 / e^2 -1 - 1

I am not sure if I did it right or is there a way to simplify my answer??
 

rand_althor

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

for integral -e to -2 of 1 -3x^2 / x - x^3 dx

I get using the result integral f'x / fx dx = log(fx)

the answer

log ( 6 / e^3 - e )

but in the answer it says log 6 / e^2 -1 - 1

I am not sure if I did it right or is there a way to simplify my answer??

 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

For some reason I keep getting a negative in front of the 12.

My answer : - 12 - 4log4

The answer: 12 - 4log4

Question Find the area bewteen the are in the first quadrant enclosed between the two curves.

y = 4 /x and y = 1 + 4x - x^2

so

A = Integral 1 to 4 ( 1 + 4x - x^2 - 4/x) dx

= [ x + 2x - 1/3 x^3 - 4logx] 1 to 4

= ( - 28/3 - 4log4) - 8/3

= -12 - 4log4

Not sure where I have gone wrong??
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

For some reason I keep getting a negative in front of the 12.

My answer : - 12 - 4log4

The answer: 12 - 4log4

Question Find the area bewteen the are in the first quadrant enclosed between the two curves.

y = 4 /x and y = 1 + 4x - x^2

so

A = Integral 1 to 4 ( 1 + 4x - x^2 - 4/x) dx

= [ x + 2x - 1/3 x^3 - 4logx] 1 to 4

= ( - 28/3 - 4log4) - 8/3

= -12 - 4log4

Not sure where I have gone wrong??
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

how is 2^n+1 - 2^n = 2^n

What indices law is that??
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Why is the integral of e^kx = 1/k . e^kx

isnt it just e^kx . k

why is there a fraction ??
 

rand_althor

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

 
Last edited:

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

It is known that f'(x) = e^x + 1/e and that f(-1) = -1 . Find f(0)

Integral e^x + 1/e dx

= e^x + loge + C

so

e^-1 + 1 + C = -1

C = - 1/e - 2

So I get

f(x) = e^x - 1/e - 1

However the answer has and x over the fraction. I can't see where I have gone wrong in my working?

ANSWER: f(x) = e^x - x/e - 1
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

It is known that f'(x) = e^x + 1/e and that f(-1) = -1 . Find f(0)

Integral e^x + 1/e dx

= e^x + loge + C

so

e^-1 + 1 + C = -1

C = - 1/e - 2

So I get

f(x) = e^x - 1/e - 1

However the answer has and x over the fraction. I can't see where I have gone wrong in my working?

ANSWER: f(x) = e^x - x/e - 1
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

for the equation y = -e^2-x + e^2 + 1

How do you work out the horizontal asymptote.

The answer is e^2 + 1
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Not sure how to find teh primative of 1 /x^1/2 - xe^-x^2
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Not sure how to find teh primative of 1 /x^1/2 - xe^-x^2
Standard integration of a power of x for the first one, and reverse chain rule for the second.
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

how do you find primative of log (e^2kx)
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

so differentiate xlogx

I get how d/dx (xlogx) = 1 + logx

Product rule

And so reversing this;

integral of ( 1 + logx) dx = xlogx + C

This next step i don't get

Integral of logx dx = xlogx - x + C

I don't get how to get the -x and where did the 1 go??
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

so differentiate xlogx

I get how d/dx (xlogx) = 1 + logx

Product rule

And so reversing this;

integral of ( 1 + logx) dx = xlogx + C

This next step i don't get

Integral of logx dx = xlogx - x + C

I don't get how to get the -x and where did the 1 go??










 

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